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<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.covariance</span></code>.LedoitWolf</a><ul>
<li><a class="reference internal" href="#examples-using-sklearn-covariance-ledoitwolf">Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.covariance.LedoitWolf</span></code></a></li>
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  <div class="section" id="sklearn-covariance-ledoitwolf">
<h1><a class="reference internal" href="../classes.html#module-sklearn.covariance" title="sklearn.covariance"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.covariance</span></code></a>.LedoitWolf<a class="headerlink" href="#sklearn-covariance-ledoitwolf" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="sklearn.covariance.LedoitWolf">
<em class="property">class </em><code class="sig-prename descclassname">sklearn.covariance.</code><code class="sig-name descname">LedoitWolf</code><span class="sig-paren">(</span><em class="sig-param">store_precision=True</em>, <em class="sig-param">assume_centered=False</em>, <em class="sig-param">block_size=1000</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/covariance/_shrunk_covariance.py#L321"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf" title="Permalink to this definition">¶</a></dt>
<dd><p>LedoitWolf Estimator</p>
<p>Ledoit-Wolf is a particular form of shrinkage, where the shrinkage
coefficient is computed using O. Ledoit and M. Wolf’s formula as
described in “A Well-Conditioned Estimator for Large-Dimensional
Covariance Matrices”, Ledoit and Wolf, Journal of Multivariate
Analysis, Volume 88, Issue 2, February 2004, pages 365-411.</p>
<p>Read more in the <a class="reference internal" href="../covariance.html#shrunk-covariance"><span class="std std-ref">User Guide</span></a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>store_precision</strong><span class="classifier">bool, default=True</span></dt><dd><p>Specify if the estimated precision is stored.</p>
</dd>
<dt><strong>assume_centered</strong><span class="classifier">bool, default=False</span></dt><dd><p>If True, data will not be centered before computation.
Useful when working with data whose mean is almost, but not exactly
zero.
If False (default), data will be centered before computation.</p>
</dd>
<dt><strong>block_size</strong><span class="classifier">int, default=1000</span></dt><dd><p>Size of the blocks into which the covariance matrix will be split
during its Ledoit-Wolf estimation. This is purely a memory
optimization and does not affect results.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Attributes</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>location_</strong><span class="classifier">array-like, shape (n_features,)</span></dt><dd><p>Estimated location, i.e. the estimated mean.</p>
</dd>
<dt><strong>covariance_</strong><span class="classifier">array-like, shape (n_features, n_features)</span></dt><dd><p>Estimated covariance matrix</p>
</dd>
<dt><strong>precision_</strong><span class="classifier">array-like, shape (n_features, n_features)</span></dt><dd><p>Estimated pseudo inverse matrix.
(stored only if store_precision is True)</p>
</dd>
<dt><strong>shrinkage_</strong><span class="classifier">float, 0 &lt;= shrinkage &lt;= 1</span></dt><dd><p>Coefficient in the convex combination used for the computation
of the shrunk estimate.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>The regularised covariance is:</p>
<p>(1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features)</p>
<p>where mu = trace(cov) / n_features
and shrinkage is given by the Ledoit and Wolf formula (see References)</p>
<p class="rubric">References</p>
<p>“A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices”,
Ledoit and Wolf, Journal of Multivariate Analysis, Volume 88, Issue 2,
February 2004, pages 365-411.</p>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sklearn.covariance</span> <span class="kn">import</span> <span class="n">LedoitWolf</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">real_cov</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="o">.</span><span class="mi">4</span><span class="p">,</span> <span class="o">.</span><span class="mi">2</span><span class="p">],</span>
<span class="gp">... </span>                     <span class="p">[</span><span class="o">.</span><span class="mi">2</span><span class="p">,</span> <span class="o">.</span><span class="mi">8</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">multivariate_normal</span><span class="p">(</span><span class="n">mean</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<span class="gp">... </span>                                  <span class="n">cov</span><span class="o">=</span><span class="n">real_cov</span><span class="p">,</span>
<span class="gp">... </span>                                  <span class="n">size</span><span class="o">=</span><span class="mi">50</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">cov</span> <span class="o">=</span> <span class="n">LedoitWolf</span><span class="p">()</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">cov</span><span class="o">.</span><span class="n">covariance_</span>
<span class="go">array([[0.4406..., 0.1616...],</span>
<span class="go">       [0.1616..., 0.8022...]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">cov</span><span class="o">.</span><span class="n">location_</span>
<span class="go">array([ 0.0595... , -0.0075...])</span>
</pre></div>
</div>
<p class="rubric">Methods</p>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.LedoitWolf.error_norm" title="sklearn.covariance.LedoitWolf.error_norm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">error_norm</span></code></a>(self, comp_cov[, norm, scaling, …])</p></td>
<td><p>Computes the Mean Squared Error between two covariance estimators.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.covariance.LedoitWolf.fit" title="sklearn.covariance.LedoitWolf.fit"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code></a>(self, X[, y])</p></td>
<td><p>Fits the Ledoit-Wolf shrunk covariance model according to the given training data and parameters.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.LedoitWolf.get_params" title="sklearn.covariance.LedoitWolf.get_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code></a>(self[, deep])</p></td>
<td><p>Get parameters for this estimator.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.covariance.LedoitWolf.get_precision" title="sklearn.covariance.LedoitWolf.get_precision"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_precision</span></code></a>(self)</p></td>
<td><p>Getter for the precision matrix.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.LedoitWolf.mahalanobis" title="sklearn.covariance.LedoitWolf.mahalanobis"><code class="xref py py-obj docutils literal notranslate"><span class="pre">mahalanobis</span></code></a>(self, X)</p></td>
<td><p>Computes the squared Mahalanobis distances of given observations.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.covariance.LedoitWolf.score" title="sklearn.covariance.LedoitWolf.score"><code class="xref py py-obj docutils literal notranslate"><span class="pre">score</span></code></a>(self, X_test[, y])</p></td>
<td><p>Computes the log-likelihood of a Gaussian data set with <code class="docutils literal notranslate"><span class="pre">self.covariance_</span></code> as an estimator of its covariance matrix.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.covariance.LedoitWolf.set_params" title="sklearn.covariance.LedoitWolf.set_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code></a>(self, \*\*params)</p></td>
<td><p>Set the parameters of this estimator.</p></td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="sklearn.covariance.LedoitWolf.__init__">
<code class="sig-name descname">__init__</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">store_precision=True</em>, <em class="sig-param">assume_centered=False</em>, <em class="sig-param">block_size=1000</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/covariance/_shrunk_covariance.py#L397"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.__init__" title="Permalink to this definition">¶</a></dt>
<dd><p>Initialize self.  See help(type(self)) for accurate signature.</p>
</dd></dl>

<dl class="method">
<dt id="sklearn.covariance.LedoitWolf.error_norm">
<code class="sig-name descname">error_norm</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">comp_cov</em>, <em class="sig-param">norm='frobenius'</em>, <em class="sig-param">scaling=True</em>, <em class="sig-param">squared=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/covariance/_empirical_covariance.py#L235"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.error_norm" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the Mean Squared Error between two covariance estimators.
(In the sense of the Frobenius norm).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>comp_cov</strong><span class="classifier">array-like of shape (n_features, n_features)</span></dt><dd><p>The covariance to compare with.</p>
</dd>
<dt><strong>norm</strong><span class="classifier">str</span></dt><dd><p>The type of norm used to compute the error. Available error types:
- ‘frobenius’ (default): sqrt(tr(A^t.A))
- ‘spectral’: sqrt(max(eigenvalues(A^t.A))
where A is the error <code class="docutils literal notranslate"><span class="pre">(comp_cov</span> <span class="pre">-</span> <span class="pre">self.covariance_)</span></code>.</p>
</dd>
<dt><strong>scaling</strong><span class="classifier">bool</span></dt><dd><p>If True (default), the squared error norm is divided by n_features.
If False, the squared error norm is not rescaled.</p>
</dd>
<dt><strong>squared</strong><span class="classifier">bool</span></dt><dd><p>Whether to compute the squared error norm or the error norm.
If True (default), the squared error norm is returned.
If False, the error norm is returned.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>The Mean Squared Error (in the sense of the Frobenius norm) between</dt><dd></dd>
<dt><code class="docutils literal notranslate"><span class="pre">self</span></code> and <code class="docutils literal notranslate"><span class="pre">comp_cov</span></code> covariance estimators.</dt><dd></dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.covariance.LedoitWolf.fit">
<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">X</em>, <em class="sig-param">y=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/covariance/_shrunk_covariance.py#L403"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Fits the Ledoit-Wolf shrunk covariance model
according to the given training data and parameters.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">array-like of shape (n_samples, n_features)</span></dt><dd><p>Training data, where n_samples is the number of samples
and n_features is the number of features.</p>
</dd>
<dt><strong>y</strong></dt><dd><p>not used, present for API consistence purpose.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">object</span></dt><dd></dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.covariance.LedoitWolf.get_params">
<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/base.py#L173"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.get_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Get parameters for this estimator.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>deep</strong><span class="classifier">bool, default=True</span></dt><dd><p>If True, will return the parameters for this estimator and
contained subobjects that are estimators.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>params</strong><span class="classifier">mapping of string to any</span></dt><dd><p>Parameter names mapped to their values.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.covariance.LedoitWolf.get_precision">
<code class="sig-name descname">get_precision</code><span class="sig-paren">(</span><em class="sig-param">self</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/covariance/_empirical_covariance.py#L161"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.get_precision" title="Permalink to this definition">¶</a></dt>
<dd><p>Getter for the precision matrix.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>precision_</strong><span class="classifier">array-like</span></dt><dd><p>The precision matrix associated to the current covariance object.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.covariance.LedoitWolf.mahalanobis">
<code class="sig-name descname">mahalanobis</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">X</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/covariance/_empirical_covariance.py#L287"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.mahalanobis" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the squared Mahalanobis distances of given observations.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">array-like of shape (n_samples, n_features)</span></dt><dd><p>The observations, the Mahalanobis distances of the which we
compute. Observations are assumed to be drawn from the same
distribution than the data used in fit.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>dist</strong><span class="classifier">array, shape = [n_samples,]</span></dt><dd><p>Squared Mahalanobis distances of the observations.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.covariance.LedoitWolf.score">
<code class="sig-name descname">score</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">X_test</em>, <em class="sig-param">y=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/covariance/_empirical_covariance.py#L205"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.score" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the log-likelihood of a Gaussian data set with
<code class="docutils literal notranslate"><span class="pre">self.covariance_</span></code> as an estimator of its covariance matrix.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X_test</strong><span class="classifier">array-like of shape (n_samples, n_features)</span></dt><dd><p>Test data of which we compute the likelihood, where n_samples is
the number of samples and n_features is the number of features.
X_test is assumed to be drawn from the same distribution than
the data used in fit (including centering).</p>
</dd>
<dt><strong>y</strong></dt><dd><p>not used, present for API consistence purpose.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>res</strong><span class="classifier">float</span></dt><dd><p>The likelihood of the data set with <code class="docutils literal notranslate"><span class="pre">self.covariance_</span></code> as an
estimator of its covariance matrix.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.covariance.LedoitWolf.set_params">
<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">**params</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/base.py#L205"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.covariance.LedoitWolf.set_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Set the parameters of this estimator.</p>
<p>The method works on simple estimators as well as on nested objects
(such as pipelines). The latter have parameters of the form
<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
component of a nested object.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>**params</strong><span class="classifier">dict</span></dt><dd><p>Estimator parameters.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">object</span></dt><dd><p>Estimator instance.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

</dd></dl>

<div class="section" id="examples-using-sklearn-covariance-ledoitwolf">
<h2>Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.covariance.LedoitWolf</span></code><a class="headerlink" href="#examples-using-sklearn-covariance-ledoitwolf" title="Permalink to this headline">¶</a></h2>
<div class="sphx-glr-thumbcontainer" tooltip="The usual covariance maximum likelihood estimate can be regularized using shrinkage. Ledoit and..."><div class="figure align-default" id="id1">
<img alt="../../_images/sphx_glr_plot_lw_vs_oas_thumb.png" src="../../_images/sphx_glr_plot_lw_vs_oas_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/covariance/plot_lw_vs_oas.html#sphx-glr-auto-examples-covariance-plot-lw-vs-oas-py"><span class="std std-ref">Ledoit-Wolf vs OAS estimation</span></a></span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="When working with covariance estimation, the usual approach is to use a maximum likelihood esti..."><div class="figure align-default" id="id2">
<img alt="../../_images/sphx_glr_plot_covariance_estimation_thumb.png" src="../../_images/sphx_glr_plot_covariance_estimation_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/covariance/plot_covariance_estimation.html#sphx-glr-auto-examples-covariance-plot-covariance-estimation-py"><span class="std std-ref">Shrinkage covariance estimation: LedoitWolf vs OAS and max-likelihood</span></a></span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="Probabilistic PCA and Factor Analysis are probabilistic models. The consequence is that the lik..."><div class="figure align-default" id="id3">
<img alt="../../_images/sphx_glr_plot_pca_vs_fa_model_selection_thumb.png" src="../../_images/sphx_glr_plot_pca_vs_fa_model_selection_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/decomposition/plot_pca_vs_fa_model_selection.html#sphx-glr-auto-examples-decomposition-plot-pca-vs-fa-model-selection-py"><span class="std std-ref">Model selection with Probabilistic PCA and Factor Analysis (FA)</span></a></span><a class="headerlink" href="#id3" title="Permalink to this image">¶</a></p>
</div>
</div><div class="clearer"></div></div>
</div>


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